Question

Using integration, find the area of the region bounded by the curves y = √(4 - x²), x² + y² - 4x = 0 and the X-axis.

Answer 1

Give, equation of curves are

y = √(4 - x²).........(i)

x² + y² - 4x = 0.......(ii)

Consider the curve

y = √(4 - x²) = y² = 4 - x²

y² + x² = 0 which represents a circle with centre (0, 0) and radius 2 units.

Now, consider the curve x² + y² - 4x = 0 which

also represents a circle with centre (2, 0) and radius 2 units.

Now Let us sketch the graph of given curves and find their points of intersection.

On substituting the value of y from Eq. (i) in Eq. (ii), we get

Clearly, required area = Area of shaded region OABO